Variations of Rigidity for Ordered Theories
Вариации жесткости для упорядоченных теорий
Kulpeshov B.Sh. Sudoplatov S.V.
2024Irkutsk State University
Bulletin of Irkutsk State University, Series Mathematics
2024#48129 - 144 pp.
One of the important characteristics of structures is degrees of semantic and syntactic rigidity, as well as indices of rigidity, showing how much the given structure differs from semantically rigid structures, i.e., structures with one-element automorphism groups, as well as syntactically rigid structures, i.e., structures covered by definable closure of the empty set. Issues of describing the degrees and indices of rigidity represents interest both in a general context and in relation to ordering theories and their models. In the given paper, we study possibilities for semantic and syntactic rigidity for ordered theories, i.e., the rigidity with respect to automorphism group and with respect to definable closure. We describe values for indices and degrees of semantic and syntactic rigidity for well-ordered sets, for discrete, dense, and mixed orders and for countable models of ℵ0-categorical weakly o-minimal theories. All possibilities for degrees of rigidity for countable linear orderings are described.
definable closure , degree of rigidity , ordered theory , semantic rigidity , syntactic rigidity
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Kazakh British Technical University, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Novosibirsk State Technical University, Novosibirsk, Russian Federation
Sobolev Institute of Mathematics, Novosibirsk, Russian Federation
Kazakh British Technical University
Institute of Mathematics and Mathematical Modeling
Novosibirsk State Technical University
Sobolev Institute of Mathematics
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